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Cosmological correlators encode statistical properties of the initial conditions of our universe. Mathematically, they can often be written as Mellin integrals of a certain rational function associated to graphs, namely the flat space…
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We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions.…
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We generalize the energy-based discontinuous Galerkin method proposed in [SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave equations. A stability and convergence analysis is presented along with numerical…
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate…
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In the paper, the authors establish Maclaurin's series expansions and series identities for positive integer powers of the inverse sine function, for positive integer powers of the inverse hyperbolic sine function, for the composite of…
We present a novel hyperbolic reformulation of the Serre-Green-Naghdi (SGN) model for the description of dispersive water waves. Contrarily to the classical Boussinesq-type models, it contains only first order derivatives, thus allowing to…
We establish a relative trace formula on $\mathrm{GL}(n+1)$ weighted by cusp forms on $\mathrm{GL}(n)$ over number fields. The spectral side is a weighted average of Rankin-Selberg $L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$…
We present a hybrid continuous and discontinuous Galerkin spectral element approximation that leverages the advantages of each approach. The continuous Galerkin approximation is used on interior element faces where the equation properties…